Two-Dimensional Gel Electrophoresis Image Analysis

Gel-based proteomics is still quite widespread due to its high-resolution power; the experimental approach is based on differential analysis, where groups of samples (e.g., control vs diseased) are compared to identify panels of potential biomarkers. However, the reliability of the result of the differential analysis is deeply influenced by 2D-PAGE maps image analysis procedures. The analysis of 2D-PAGE images consists of several steps, such as image preprocessing, spot detection and quantitation, image warping and alignment, spot matching. Several approaches are present in literature, and classical or last-generation commercial software packages exploit different algorithms for each step of the analysis. Here, the most widespread approaches and a comparison of the different strategies are presented.

2D-DIGE and Fluorescence Image Analysis

2D-DIGE is still a very widespread technique in proteomics for the identification of panels of biomarkers, allowing to tackle with some important drawback of classical two-dimensional gel-electrophoresis. However, once 2D-gels are obtained, they must undergo a quite articulated multistep image analysis procedure before the final differential analysis via statistical mono- and multivariate methods. Here, the main steps of image analysis software are described and the most recent procedures reported in the literature are briefly presented.

GENOCOP Algorithm and Hierarchical Grid Transformation for Image Warping of Two-Dimensional Gel Electrophoretic Maps

Hierarchical grid transformation is a powerful hierarchical approach to 2-D map warping, able to model both global and local deformations. The algorithm can be stopped when a desired degree of accuracy in the images alignment is obtained. The deformed image is warped and aligned to the target image using a grid where the number of nodes increases in each step of the algorithm. The numerical optimization of the position of the nodes of the grid can be efficiently solved by genetic algorithms, ensuring the achievement of the optimal position of the nodes with a low computational cost with respect to other methods. Here, the optimization of the position of the nodes is carried out by GENOCOP (genetic algorithm for numerical optimization of constrained problems), refined by the following conjugate gradient optimization step. The modeling of the warped space is then achieved by a spline model where some constraints are introduced in the choice of the nodes that are moved. The whole procedure can be intended as an evolutionary method that models the deformation of the gel map at different levels of detail.

Image Pretreatment Tools II: Normalization Techniques for 2-DE and 2-D DIGE

Gel electrophoresis is usually applied to identify different protein expression profiles in biological samples (e.g., control vs. pathological, control vs. treated). Information about the effect to be investigated (a pathology, a drug, a ripening effect, etc.) is however generally confounded with experimental variability that is quite large in 2-DE and may arise from small variations in the sample preparation, reagents, sample loading, electrophoretic conditions, staining and image acquisition. Obtaining valid quantitative estimates of protein abundances in each map, before the differential analysis, is therefore fundamental to provide robust candidate biomarkers. Normalization procedures are applied to reduce experimental noise and make the images comparable, improving the accuracy of differential analysis. Certainly, they may deeply influence the final results, and to this respect they have to be applied with care. Here, the most widespread normalization procedures are described both for what regards the applications to 2-DE and 2D Difference Gel-electrophoresis (2-D DIGE) maps.

Image Pretreatment Tools I: Algorithms for Map Denoising and Background Subtraction Methods

One of the critical steps in two-dimensional electrophoresis (2-DE) image pre-processing is the denoising, that might aggressively affect either spot detection or pixel-based methods. The Median Modified Wiener Filter (MMWF), a new nonlinear adaptive spatial filter, resulted to be a good denoising approach to use in practice with 2-DE. MMWF is suitable for global denoising, and contemporary for the removal of spikes and Gaussian noise, being its best setting invariant on the type of noise. The second critical step rises because of the fact that 2-DE gel images may contain high levels of background, generated by the laboratory experimental procedures, that must be subtracted for accurate measurements of the proteomic optical density signals. Here we discuss an efficient mathematical method for background estimation, that is suitable to work even before the 2-DE image spot detection, and it is based on the 3D mathematical morphology (3DMM) theory.

Differential Analysis of 2-D Maps by Pixel-Based Approaches

Two approaches to the analysis of 2-D maps are available: the first one involves a step of spot detection on each gel image; the second one is based instead on the direct differential analysis of 2-D map images, following a pixel-based procedure. Both approaches strongly depend on the proper alignment of the gel images, but the pixel-based approach allows to solve important drawbacks of the spot-volume procedure, i.e., the problem of missing data and of overlapping spots. However, this approach is quite computationally intensive and requires the use of algorithms able to separate the information (i.e., spot-related information) from the background. Here, the most recent pixel-based approaches are described.

GENOCOP algorithm and hierarchical grid transformation for image warping of two dimensional gel eletrophoretic maps

Hierarchical grid transformation is a powerful approach to SDS 2DPAGE maps warping. The hierarchy of the warping transformation is able to model both global and local deformations of the gels and the algorithm can be stopped when a certain degree of accuracy in the image alignment is obtained. The numerical optimization of the position of the nodes of the grid that are responsible for the image warping is a multivariate task that can be solved efficiently using Genetic Algorithms. The use of Genetic Algorithms ensures that an optimal position of the nodes can be defined with a low computational cost with respect to other methods. The optimal positions of the nodes of the grid can be successfully used for defining a good warping of the gels.

Analyzing 2D gel images using a two-component empirical Bayes model

Background

Two-dimensional polyacrylomide gel electrophoresis (2D gel, 2D PAGE, 2-DE) is a powerful tool for analyzing the proteome of a organism. Differential analysis of 2D gel images aims at finding proteins that change under different conditions, which leads to large-scale hypothesis testing as in microarray data analysis. Two-component empirical Bayes (EB) models have been widely discussed for large-scale hypothesis testing and applied in the context of genomic data. They have not been implemented for the differential analysis of 2D gel data. In the literature, the mixture and null densities of the test statistics are estimated separately. The estimation of the mixture density does not take into account assumptions about the null density. Thus, there is no guarantee that the estimated null component will be no greater than the mixture density as it should be.

Results

We present an implementation of a two-component EB model for the analysis of 2D gel images. In contrast to the published estimation method, we propose to estimate the mixture and null densities simultaneously using a constrained estimation approach, which relies on an iteratively re-weighted least-squares algorithm. The assumption about the null density is naturally taken into account in the estimation of the mixture density. This strategy is illustrated using a set of 2D gel images from a factorial experiment. The proposed approach is validated using a set of simulated gels.

Conclusions

The two-component EB model is a very useful for large-scale hypothesis testing. In proteomic analysis, the theoretical null density is often not appropriate. We demonstrate how to implement a two-component EB model for analyzing a set of 2D gel images. We show that it is necessary to estimate the mixture density and empirical null component simultaneously. The proposed constrained estimation method always yields valid estimates and more stable results. The proposed estimation approach proposed can be applied to other contexts where large-scale hypothesis testing occurs.

Region-based Statistical Analysis of 2D PAGE Images

A new comprehensive procedure for statistical analysis of two-dimensional polyacrylamide gel electrophoresis (2D PAGE) images is proposed, including protein region quantification, normalization and statistical analysis. Protein regions are defined by the master watershed map that is obtained from the mean gel. By working with these protein regions, the approach bypasses the current bottleneck in the analysis of 2D PAGE images: it does not require spot matching. Background correction is implemented in each protein region by local segmentation. Two-dimensional locally weighted smoothing (LOESS) is proposed to remove any systematic bias after quantification of protein regions. Proteins are separated into mutually independent sets based on detected correlations, and a multivariate analysis is used on each set to detect the group effect. A strategy for multiple hypothesis testing based on this multivariate approach combined with the usual Benjamini-Hochberg FDR procedure is formulated and applied to the differential analysis of 2D PAGE images. Each step in the analytical protocol is shown by using an actual dataset. The effectiveness of the proposed methodology is shown using simulated gels in comparison with the commercial software packages PDQuest and Dymension. We also introduce a new procedure for simulating gel images.

Computational methods for analysis of two-dimensional gels

Two-dimensional gel electrophoresis (2D gels) is an essential quantitative proteomics technique that is frequently used to study differences between samples of clinical relevance. Although considered to have a low throughput, 2D gels can separate thousands of proteins in one gel, making it a good complementary method to MS-based protein quantification. The main drawback of the technique is the tendency of large and hydrophobic proteins such as membrane proteins to precipitate in the isoelectric focusing step. Furthermore, tests using different programs with distinct algorithms for 2D-gel analysis have shown inconsistent ratio values. The aim here is therefore to provide a discussion of algorithms described for the analysis of 2D gels.

Median-modified Wiener filter provides efficient denoising, preserving spot edge and morphology in 2-DE image processing

Denoising is a fundamental early stage in 2-DE image analysis strongly influencing spot detection or pixel-based methods. A novel nonlinear adaptive spatial filter (median-modified Wiener filter, MMWF), is here compared with five well-established denoising techniques (Median, Wiener, Gaussian, and Polynomial-Savitzky-Golay filters; wavelet denoising) to suggest, by means of fuzzy sets evaluation, the best denoising approach to use in practice. Although median filter and wavelet achieved the best performance in spike and Gaussian denoising respectively, they are unsuitable for contemporary removal of different types of noise, because their best setting is noise-dependent. Vice versa, MMWF that arrived second in each single denoising category, was evaluated as the best filter for global denoising, being its best setting invariant of the type of noise. In addition, median filter eroded the edge of isolated spots and filled the space between close-set spots, whereas MMWF because of a novel filter effect (drop-off-effect) does not suffer from erosion problem, preserves the morphology of close-set spots, and avoids spot and spike fuzzyfication, an aberration encountered for Wiener filter. In our tests, MMWF was assessed as the best choice when the goal is to minimize spot edge aberrations while removing spike and Gaussian noise.

A new method for assigning common spot boundaries for multiple gels in two-dimensional gel electrophoresis

The benefits of defining common spot boundaries when several gels from 2-DE are compared and analyzed have lately been stressed by both commercial software producers and users of this software. Though the importance of common spot boundaries is clearly stated, few reports exist that target this issue explicitly. In this study a method for defining common spots boundaries is developed, called the spot density method. The method consists of the following steps: segmentation and spot identification on each individual gel, transferring the spot-center coordinates for all gels onto a single new gel, collecting spot centers clustered together in the new gel and finally assigning pixels and new spot boundaries based on the spots in each cluster. The method is compared to a synthetic gel approach, and validated by visual inspection of three representative areas in the gels. The gel images need to be aligned prior to segmentation and spot identification, but the method can be used regardless of the choice of segmentation procedure. This makes the method an easy extension to existing methods for spot identification and matching. Conclusions based on the visual inspection are that the spot density method identifies partly overlapping spots and low-intensity spots better than the synthetic gel approach.

Lights, Camera, Action! Systematic variation in 2-D difference gel electrophoresis images

2-D Difference gel electrophoresis (DIGE) circumvents many of the problems associated with gel comparison via the traditional 2-DE approach. DIGE's accuracy and precision, however, is compromised by the existence of other significant sources of systematic variation, including that caused by the apparatus used for imaging proteins (location of the camera and lighting units, background material, imperfections within that material, etc.). Through a series of experiments, we estimate some of these factors, and account for their effect on the DIGE experimental data, thus providing improved estimates of the true relative protein intensities. The model presented here includes 2-DE images as a special case.

Adaptive contrast enhancement of two-dimensional electrophoretic protein gel images facilitates visualization, orientation and alignment

2-DE is a powerful technique to discriminate post-translationally modified protein isoforms. However, all steps of 2-DE preparation and gel-staining may introduce unwanted artefacts, including inconsistent variation of background intensity over the entire 2-DE gel image. Background intensity variations limit the accuracy of gel orientation, overlay alignment and spot detection methods. We present a compact and efficient denoising algorithm that adaptively enhances the image contrast and then, through thresholding and median filtering, removes the gray-scale range covering the background. Applicability of the algorithm is demonstrated on immunoblots, isotope-labeled gels, and protein-stained gels. Validation is performed in contexts of (i) automatic gel orientation based on Hough transformation, (ii) overlay alignment based on cross correlation and (iii) spot detection. In gel stains with low background variability, e.g. Sypro Ruby, denoising will lower the spot detection sensitivity. In gel regions with high background levels denoising enhances spot detection. We propose that the denoising algorithm prepares images with high background for further automatic analysis, without requiring manual input on a gel-to-gel basis.

Correlation analysis of two-dimensional gel electrophoretic protein patterns and biological variables

BACKGROUND

Two-dimensional gel electrophoresis (2DE) is a powerful technique to examine post-translational modifications of complexly modulated proteins. Currently, spot detection is a necessary step to assess relations between spots and biological variables. This often proves time consuming and difficult when working with non-perfect gels. We developed an analysis technique to measure correlation between 2DE images and biological variables on a pixel by pixel basis. After image alignment and normalization, the biological parameters and pixel values are replaced by their specific rank. These rank adjusted images and parameters are then put into a standard linear Pearson correlation and further tested for significance and variance.

RESULTS

We validated this technique on a set of simulated 2DE images, which revealed also correct working under the presence of normalization factors. This was followed by an analysis of p53 2DE immunoblots from cancer cells, known to have unique signaling networks. Since p53 is altered through these signaling networks, we expected to find correlations between the cancer type (acute lymphoblastic leukemia and acute myeloid leukemia) and the p53 profiles. A second correlation analysis revealed a more complex relation between the differentiation stage in acute myeloid leukemia and p53 protein isoforms.

CONCLUSION

The presented analysis method measures relations between 2DE images and external variables without requiring spot detection, thereby enabling the exploration of biosignatures of complex signaling networks in biological systems.

Protein Image Alignment via Piecewise Affine Transformations

We present a new approach for aligning families of 2D gels. Instead of choosing one of the gels as reference and performing a pairwise alignment, we construct an ideal gel that is representative of the entire family and obtain a set of piecewise affine transformations that optimally align each gel of the family to the ideal gel. The coefficients defining the transformations as well as the ideal landmarks are obtained as the solution of a large-scale quadratic programming problem that can be solved efficiently by interior-point methods.

Matching 2D gel electrophoresis images

Automatic alignment (matching) of two-dimensional gel electrophoresis images is of primary interest in the field of proteomics. The proposed method of 2D gel image matching is based on fuzzy alignment of features, extracted from gels' images, and it allows both global and local interpolation of image grid, followed by brightness interpolation. Method performance is tested on simulated images and gel images available via the Internet databases.

Warping two-dimensional electrophoresis gel images to correct for geometric distortions of the spot pattern

A crucial step in two-dimensional gel based protein expression analysis is to match spots in different gel images that correspond to the same protein. It still requires extensive and time-consuming manual interference, although several semiautomatic techniques exist. Geometric distortion of the protein patterns inherent to the electrophoresis procedure is one of the main causes of these difficulties. An image warping method to reduce this problem is presented. A warping is a function that deforms images by mapping between image domains. The method proceeds in two steps. Firstly, a simple physicochemical model is formulated and applied for warping of each gel image to correct for what might be one of the main causes of the distortions: current leakage across the sides during the second-dimensional electrophoresis. Secondly, the images are automatically aligned by maximizing a penalized likelihood criterion. The method is applied to a set of ten gel images showing the radioactively labeled proteome of yeast Saccharomyces cerevisiae during normal and steady-state saline growth. The improvement in matching when given the warped images instead of the original ones is exemplified by a comparison within a commercially available software.